I think here's the problematic code
The series expansion of $e^z$
is given by
\[ e^z = \displaystyle \sum^{\infty}_{n=0} \dfrac{z^n}{n!}\]
Then we can write the given function as
\begin*{align}
\frac{e^z - 1}{z^2} &= \frac{e^z}{z^2} - \frac{1}{z^2} \\
&= \frac{1}{z^2} \left( 1 + z + \frac{z^2}{2!} + \frac{z^3}{3!} + \cdots \right) + \frac{1}{z^2} \\
&= \frac{z}{z^2} + \frac{1}{2} + \frac{z}{3!} + \frac{z^2}{4!} + \cdots \\
&= \frac{1}{z} + \frac{1}{2} \frac{z}{3!} + \displaystyle
\sum^{\infty}_{k=2} \frac{z^k}{(k+2)!}
\end*{align}
The error messages include "! extra } or missing $" and "! Misplaced alignment tab character &"
. It's 3 AM here, so I apologize if I’ve missed a missing $
or {}
but I really don't see what the error is here. I have tried changing the formatting so that I delete all the white space but it doesn't seem to help either.
Thank you
\displaystyle
with both inputs, after correcting\begin*{align}
and\end*{align}
into\begin{align*}
and\end{align*}
. Also\cdots
should be\dotsb
.